WASHINGTON — Lifting a stay of execution it granted four months ago, the Supreme Court on Monday turned down the final appeal of a retarded Louisiana man who as a teen-ager was convicted of killing a state trooper.

The court's action, taken without comment, allows Louisiana to execute Dalton Prejean. He has been on Louisiana's death row since 1978, longer than anyone else in his state's history.

The Supreme Court issued the stay on the eve of his scheduled execution last November after Gov. Buddy Roemer rejected the state pardon board's recommendation that he commute the death sentence to life imprisonment.

The purpose of the stay was to give the justices time to decide whether to hear the merits of Prejean's appeal; the stay was to expire automatically if the court decided not to take the case.

Justices William J. Brennan Jr. and Thurgood Marshall dissented Monday from the court's refusal to hear Prejean's appeal and the appeals of 12 death row prisoners from other states. They did not write opinions, noting only that they were ''adhering to our views that the death penalty is in all circumstances cruel and unusual.''

At the same time Monday, also without opinions, the court vacated the death sentences of two men on Mississippi's death row and one from Missouri.

The Prejean case attracted considerable attention last fall as Roemer was considering whether to commute the sentence. Prejean, now 31, has an IQ of 76 and was said to have had the mental capability of a 13-year-old in 1977 when he fatally shot a state trooper after he was stopped for a traffic violation.

He is black and his victim was white. All members of the jury that sentenced him to death were white; the four black prospective jurors had been barred by the prosecution through peremptory challenges.

Prejean's lawyers had filed several constitutional challenges - petitions for writs of habeas corpus - to his conviction and sentence in the federal and Louisiana courts.

Both the Louisiana Supreme Court and the U.S. 5th Circuit Court of Appeals turned down his latest petitions last fall.

Appeals from both those rulings were filed simultaneously at the Supreme Court.

Last June in two 5-4 decisions, the Supreme Court ruled that the Constitution does not forbid executing murderers who are either mentally retarded or were teen-agers at the time of the crime.

So Prejean's lawyers focused on other issues, principally whether the instructions to the jury had blocked full consideration of Prejean's mental deficiencies, and whether he could challenge the composition of the jury.